Express 9r2 = (1 + 3r cos θ)2 in rectangular coordinates. Which conic section is represented by the rectangular equation?

Q: Use the Root Test to determine the convergence or divergence of the series.

A: Given

Q: Find the second derivative of the function (r² + 1)(x² _ z +1) U =

A:

Q: Prove the identity cos6x + sin6x = 3cos*x- 3cos?x - 1

A: To Determine: prove the identity  Given: we have cos6x+sin6x=3cos4x-3cos2x-1 Explanation: we have an...

Q: Differentiate f  and find the domain of f .   f(x)   = In  In  In x

A: we have to differentiate f and also we have to find the domain of f  f(x)   = In  In  In x

Q: The function f(x) = 8x3 + 1 is all one-to-one. For the function,a. Find an equation for f -1(x), the...

A: Given: fx=8x3+1 To determine: a.f-1(x) b. Verify ff-1x=x & f-1fx=x

Q: Write a formula for the general term (the nth term) of the arithmetic sequence -7, -3, 1, 5,...........

A: Given arithmetic sequence is -7, -3, 1, 5,........ . We have to find the 20th term of the sequence. ...

Q: Use the Integral Test to determine whether the infinite series is convergent. 00 Σ 1 n² + 25 n=5 Fil...

A: To use integral test to determine the infinite series is convergent  ∑n=5∞1n2+25

Q: The profit in dollars from the sale of x expensive watches is P(x)= 0.09x-3x+4x°4 -4400. Find the ma...

A: Given: P(x)=0.09x2-3x+4x0.4-4400

Q: Sketch the region whose area is given by the definite integral. Then use a geometric formula to eval...

A: Given integral is ∫-349dx We plot it as,

Q: Calculus Question

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Q: Solve the homogeneous differential equation (x2 + y2) dx − 2xy dy = 0 in terms of x and y. A homogen...

A: Given homogeneous differential equation, x2+y2dx-2xydy=0

Q: From a point on level ground 125 feet from the base of a tower, the angle ofelevation is 57.2°. Appr...

A: let a represents the height of the tower. In the right triangle, we have a known angle, an unknown ...

Q: Use integration by parts to evaluate  ∫x cos x dx with u = x and dv = cos x dx.

A: Integration by parts: I=∫xcosx dxFormula:   ∫uvdx=u∫vdx-∫[ddx(u).∫vdx]dxHere u=x , v=cosx 

Q: Passing through (-4, 2) and perpendicular to the line whose equation is y = (1/3) x + 7.Use the give...

A: Given points are (-4,2). The equation of a line in slope intercept form is given by y=mx+b......(1) ...

Q: Calculus questions

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Q: Write the equation in its equivalent logarithmic form: 25 = x

A: Given equation 25=x......(1) Recall the logarithm identity logba=x So that bx=a Here, a=x, b=2 and x...

Q: You are choosing between two cellphone plans. Data Plan A offers a flat monthly rate of $20 per giga...

A: Equation: Plan A offers a flat monthly rate of $20 per gigabyte (GB). Data Plan B has a monthly fee ...

Q: The time, t, in weeks, needed for the population of fireflies in a field to reach p individual is gi...

A: Consider the given function tp=45ln10,00018000-p

Q: Velocity and acceleration from position Consider the following position function.a. Find the velocit...

A: Velocity & Acceleration: The velocity of the object for t∈[0,2π], is represented as v(t)=r'(t)=&...

Q: How can we find the limit of each rational function?

A: A rational function is the ratio of two polynomials.In the case of a single variable, x, a function ...

Q: Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dim...

A: Consider the provided function, fx,y=x3-3x+3xy2 Find the local maximum and minimum values and the sa...

Q: simplify(assume X>0) √(1/√81)

A: 1/sqrt(81) =1/9 or -1/9 Considering the positive square root we get, 1/sqrt(81) = 1/9 Considering th...

Q: Evaluate the definite integral. Use a graphing utility to verify your result

A: Given integral ∫45x2x-6dx Substitute  u=2x-6 Upper limit at x=5 is 2. Lower limit at x= is 2 =∫22u2+...

Q: Integration review Evaluate the following integrals.

A: Given

Q: Can you please help me with these questions.

A: Hey, since there are multiple questions posted, we will answer first question. If you want any speci...

Q: Solve the polynomial inequality 6x2 + x > 1 and graph the solution set on a real number line. Exp...

A:

Q: Chain Rule with several independent variables Find the following derivatives.

A: Given that w=x2+y2+z2, x=st, y=rs, z=rt

Q: graph the following. be sure to include the ordered pairs, including any existing x-intercepts (loga...

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Q: Solve the formula for the specified variable. Do you recognize the formula? If so, what does it desc...

A: Consider the formulas, S=P+P·r·t

Q: Use a change of variables or Table toevaluate the following indefinite integrals. Check your work by...

A:  Definition used -                 U substitution -                     ∫f(g(x))g'(x)dx =∫f(u)du ,  ...

Q: EXAMPLE 3 The surprises of a rational function Use the graphing guidelines to 10x on its domain. x? ...

A: Solution :- The given function is  f(x)=10x3x2-1.........(eq01) ⇒f(x)=10x3(x-1)(x+1)  

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(-1, 1, 5) P2(2, 5,...

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k                         .......

Q: Verify the identity: (csc x - sec x)/(csc x + sec x) = (cot x - 1)/(cot x + 1)

A: The given identity to prove is , cscx-secxcscx+secx=cotx-1cotx+1 Proof : Take LHS of the given ident...

Q: Find the critical points of the following function. Assume a is a nonzero constant.

A:

Q: People who believe in biorhythms claim that there are three cycles that rule our behavior—the physic...

A: we have been given the function of sin  E=sinπ14t

Q: Denominator may reduce the fraction to one whose denominator is no longer zero.True or false?

A: Given:Denominator may reduce the fraction to one whose denominator isno longer zero

Q: Find the slope of the line tangent to the graph of ƒ(x)

A: Consider the following function: fx=xx+6 Differentiate fx with respect to x: dfxdx=ddxxx+6=x+6ddxx-x...

Q: Heart rates and life spans of most mammals can be modeled using inverse variation. The bar graph sho...

A: Given: Heart rates and life spans of most mammals can be modeled using an inverse variation. The bar...